Calculation of the Base Flow Index
Institute of Hydrology
_______________________________________________
This report is an extract taken from Report No 108 Low
Flow Estimation in the United Kingdom, a report
published by the Natural Environment Research Council
under contract to the Department of the Environment. It
should not be quoted by third parties without permission
of both DOE and the Institute of Hydrology
_______________________________________________
Institute of Hydrology
Crowmarsh Gifford
Wallingford
Oxfordshire
OX10 8BB
Tel:
01491 83800
Fax: 01491 692424
Telex: 849365 Hydrol G
1
Base Flow Index
A number of regional low flow studies including Wright (1974), Klaassen and Pilgrim (1975), Institute
of Hydrology (1980) and Pirt and Douglas (1982,(b)) have highlighted the importance of indexing the
hydrogeology of the catchment if flows are successfully to be predicted at the ungauged site. In order to
avoid a profusion of relationships between low flow indices and catchment characteristics, the Low
Flow Studies report (Institute of Hydrology, 1980) recommended using the proportion of base flow in
the river defined by a Base Flow Index (BFI), for indexing the effect of geology on low flows. Figure 1
illustrates the method of derivation of the index using programmable smoothing and separation rules on
the daily mean flow hydrograph. Figure 2 contrasts the hydrographs and values of BFI for two
catchments with contrasting geology (values of BFI range from 0.1 for a very flashy river to nearly unity
for a very stable river with a high base flow proportion).
39027 Pang at Pangbourne
1.8
recorded hydrograph
1.6
5 day minima
base flow
Base Flow Index (BFI) = 0.892
1.2
3
-1
Daily flow (m s )
1.4
1.0
0.8
0.6
0.4
0.2
0.0
J
F
M
A
M
J
J
A
1970
Figure 1
Derivation of the Base Flow Index for the Pang (Jan – Aug 1970)
Although the index was originally related to geology and lake storage in the UK, a wider use of the
index in Canada (Pilon and Condie, 1986), Fiji (Green, 1986), Zimbabwe (Meigh, 1987), New Zealand
(National Water and Soil Conservation Authority, 1984) and Norway (Tallaksen, 1986) has shown it to
have been useful in regional flood and low flow studies. The concept has also been used in Australia
(Nathan and McMahon, 1990a) where it is used as a key variable in low flow estimation techniques.
Unlike the Low Flow Studies report (Institute of Hydrology, 1980), BFI is not used directly as a key
variable linking low flow statistics and catchment characteristics. Instead, the Base Flow Index was used
as a key variable in describing the hydrological response of catchments in order to develop the HOST
classification scheme (Boorman et al. 1991). The 29 HOST classes and URBAN and LAKE were
subsequently clustered into 12 low flow groups for use in this study. Additionally, BFI can be used for
the estimation of key low flow statistics where short periods of flow data are available.
2
Figure 2
BFI for two catchments with contrasting geology a) predominantly permeable, b)
predominantly impermeable
BASE FLOW SEPARATION PROCEDURE
The Base Flow Index (BFI) can be thought of as measuring the proportion of the river's runoff that
derives from stored sources. A computer program applies smoothing and separation rules to a recorded
3
flow hydrograph, from which the index is calculated as the ratio of the flow under the separated
hydrograph to the flow under the total hydrograph (Figure 1).
The program calculates the minima of five-day non-overlapping consecutive periods and subsequently
searches for turning points in this sequence of minima. The turning points are then connected to obtain
the base flow hydrograph, which is constrained to equal the observed hydrograph ordinate on any day
when the separated hydrograph exceeds the observed. The procedure for calculating the index is as
follows:
1.
Divide the mean daily flow data into non-overlapping blocks of five days and calculate the
minima for each of these blocks, and let them be called Q1, Q2, Q3...Qn.
2.
Consider in turn (Q1, Q2, Q3,), (Q2, Q3, Q4),...(Qi-1, Qi, Qi+1) etc. In each case, if 0.9 x central
value < outer values, then the central value is an ordinate for the base flow line. Continue this
procedure until all the data have been analysed to provide a derived set of base flow ordinates
QB1, QB2, QB3,...QBn which will have different time periods between them.
3.
By linear interpolation between each QBi value, estimate each daily value of QB1...QBn
4.
If QBi > Qi then set QBi = Qi
5.
Calculate VB the volume beneath the base flow line between the first and last base flow turning
points QB1... QBn
6.
Calculate VA the volume beneath the recorded mean daily flows Qn for the period QB1 ... QBn.
7.
The Base Flow Index is then VB/VA.
For demonstration purposes, a worked example is given in Table 1 and Table 2, and plotted in Figure 1,
using data for eight months of data for the Pang at Pangbourne (January-August 1970).
BASEFLOW LINE START AND FINISH POINTS
Baseflow separation cannot start on the first day of the data record and similarly will not finish on the
last day of record. It is important therefore to recognise that when the dates of the beginning and end of
the baseflow line have been established, then these same dates must be used in calculating the total
volume of flow beneath the hydrograph as well as in calculating the volume of flow beneath the
baseflow line.
4
Table 1
Derivation of hydrograph base flow line turning points
39027 Pang Pangbourne
Year 1970
DAY
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
1
.422
.883
.733
.665
.596
.466
.390
.310
2
.426
.941
.737
.633
.577
.357
.278
3
.421
.879
.711
.637
.580
.449
.358
.286
4
.398
.851
.810
.630
.592
.468
.359
.281
5
.389
.797
.765
.657
.580
.440
.347
.290
6
.395
.756
.768
.777
.568
.431
.341
.317
7
.364
.776
.790
.724
.628
.426
.312
8
.379
.781
.759
.699
.572
.404
9
.593
.805
.708
.675
.619
10
.775
.729
.698
.669

11
1.020
.706
.978
.653

12
.740
.813
.997
13
.630
.749
14
.988
.708
15
.740
.667
16
.708
17
.628
18





.439



.313
.424
.347
.310
.634
.428
.332
.319
.608
.431
.335
.315
.863
.641
.414
.316
.305
.859
.806
.624
.407
.308
.798
.748
.593
.367
.734
.715
.596
.673
.741
.706
.879
.785
.657
.907
19
.633
20
.628
21
.645
22


.298
.359
.299
.387
.354
.320
.563
.389
.352
.313
.735
.564
.403
.359
.291
.759
.710
.545
.408
.340
1.000
.697
.689
.581
.382
.975
.708
.649
.506
.378
1.040
.694
.682
.526
.355
.784
1.040
.686
.672
.536
23
1.550
.982
.732
.644
.418
24
1.180
.856
.734
.615
25
.937
.806
.692
26
.990
.761
.676
27
.820
.748
.638
28
.786
.731
29




.301
.379
.427
.355
.384
.347
.359
.411
.348
.349
.391
.340
.487
.443
.357
.340
.669
.488
.379
.352
.320

.647
.538
.373
.358
.310

.622
.491
.378
.333
.315
.648
.622
.517
.359
.349
.311
.856
.658
.605
.486
.358
.348
.306
30
1.280
.649
.607
.475
.370
.328
.293
31
.916
.679
.291
.280
(i)
(ii)







.485
Shaded values are 5-day minima
Ticked 5-day minima are base flow line turning points




.323
.371


.368


5
Table 2
BFI from data for Pang
1
Date of turning
point
2
Discharge
(cumecs)
3
Time span
between turning
points (days)
4
Average
discharge
(cumecs)
5
Increment of
Baseflow
(cumec-days)
7/1
17/1
21/1
.364
.628
.645
10
4
16
.496
.637
.701
4.96
2.55
11.21
6/2
11/2
15/2
28/2
.756
.706
.667
.731
5
4
13
3
.731
.687
.699
.721
3.66
2.75
9.09
2.16
3/3
10/3
15/3
21/3
26/3
27/3
.711
.698
.734
.694
.676
.638
7
5
6
5
1
8
.705
.716
.714
.685
.657
.634
4.93
3.58
4.28
3.43
0.66
5.07
4/4
10/4
11/4
20/4
24/4
29/4
.630
.669
.653
.649
.615
.605
6
1
9
4
5
3
.650
.661
.651
632
.610
.591
3.90
0.66
5.86
2.53
3.05
1.77
2/5
6/5
23/5
.577
.568
.418
4
17
10
.573
.493
.429
2.29
8.38
4.29
2/6
8/6
14/6
19/6
21/6
29/6
.439
.404
.367
.382
.355
.358
6
6
5
2
8
8
.422
.386
.375
.369
.366
.335
2.53
2.31
1.87
0.74
2.85
2.68
7/7
13/7
18/7
23/7
.312
.308
.340
.340
6
5
5
10
.310
.324
.340
.309
1.86
1.62
1.70
3.09
2/8
4/8
13/8
17/8
.278
.281
.298
.291
2
9
4
.280
.290
.295
0.56
2.61
1.18
Total volume beneath baseflow hydrograph from 7/1 to 17/8 = VB = 116.660
Total volume beneath recorded hydrograph from 7/1 to 17/8 = VA = 130.797
Baseflow index = VB/VA = .892
6
CALCULATION OF ANNUAL BFI
There are two alternative methods for calculating annual BFIs. The first is to compute the separation for
the entire record and then estimate BFI for each year. The second is to run the separation program on
year 1 and then on year 2 etc., starting each year as an entirely new record. In the latter case a few days
in early January and late December will be eliminated from the calculation for each year of record. The
two approaches differ slightly and for calculating annual values the first procedure is recommended.
CALCULATION OF PERIOD OF RECORD BFI
A mean value of BFI can be calculated from a series of annual BFIs, but this will be different from a
single value calculated from the period of record. BFI is defined as the ratio VB/VA where VB represents
the volume beneath the base flow separation line and VA represents the mean flow beneath the
hydrograph.
Ten years of record will provide ten annual values of BFI. However, the mean of these ten values will
not in general equate to the single value obtained from the entire ten years of record. This can easily be
seen by the following example, showing three years of artificial data in which `year 1' is of a very
different character.
Year 1
Year 2
Year 3
Total
VB
9.0
40.0
40.0
89.0
VA
10.0
100.0
100.0
210.0
0.9
0.4
0.4
0.424
BFI = VB/VA
Here, the mean of the three annual BFI values is 0.567 while the overall value is 0.424. The
recommended procedure is to calculate one value of BFI based on a separation of the entire record.
BFI VARIABILITY
Studies of BFI variability found that annual values of BFI were more stable than other low flow
variables. For example the coefficient of variation of annual Base Flow Index values was found to be
one-third of Q95(10) values. A more detailed study of BFI variability in Scotland (Gustard et al., 1987)
was carried out on 135 stations which had more than nine years of record. The coefficient of variation
(Figure 3.3) and the standard deviation of annual BFIs were calculated for each of the 135 stations and
the mean of these standard deviations was found to be 0.054. This finding that values estimated from
short records could be used with confidence supported the use of BFI as a key variable in low flow
estimation procedures.
A linear regression was performed for each station between annual BFI and annual runoff to test
whether wet or dry years had a tendency to give rise to low or high BFI values. Over 100 of the 135
records had values of explained variance less than 30% indicating a weak relationship between annual
BFI and annual runoff. Only 20 stations had explained variances in excess of 50% and these were
located mainly in eastern Scotland. Further investigation revealed that most of these stations had their
highest annual BFI in the drought years of 1973 and 1976.
These results suggest that although years of extreme drought may produce higher than average BFIs,
most annual BFIs are close to the long term value. Provided extreme years are avoided, the BFI can be
estimated with confidence from a short record, with an error of 0.05 being typical for estimates derived
from a single year of daily mean flow data in Scotland.
7
Figure 3
Coefficient of variation of annual BFI values in Scotland
HYDROMETRIC ERRORS AND MISSING DATA
A study was carried out to assess the influence of hydrometric errors and missing data on BFI. A bias
was applied to the gauged flow data by increasing or decreasing daily flow data to simulate hydrometric
error. The sensitivity of the derived BFI to this simulated error was then examined. The main results
were that the percentage error in BFI was less than a given percentage error in flow data and the error
was largest for catchments with low BFI values. For example, a 10% error in high flows (Q5) or low
flows (Q95) resulted in a 7% error in BFI for low BFI catchments (0.2) and less than 1% error in BFI for
high BFI (0.9) catchments.
A similar sensitivity analysis was carried out to evaluate the impact of missing data on calculated values
of BFI. The value of BFI was shown to be sensitive to missing data primarily because several days of
data are omitted from the base flow separation as a result of only 1 missing day of gauged data. It was
concluded that improvement in BFI estimation is achieved by interpolating up to a maximum of 5
missing days. However BFI values must be used with caution if the record contains several gaps (more
than 2% of the record).
8
References
Boorman, D.B. & Hollis, J.M. 1990. Hydrology of Soil Types. A hydrologically-based classification of
the soils of England and Wales. MAFF conference of river and coastal engineers, Loughborough
University.
Boorman, D.B., Hollis, J.M. & Lilly, A. 1991. The production of the Hydrology of Soil Types (HOST)
data set. BHS Third National Symposium, Southampton, 6.7-6.13.
Green, C.S. 1986. Preliminary notes on the processing and analysis of hydrological data for
groundwater assessment. Dept. of Mineral Resources Internal Document, Govt. of Fiji.
Institute of Hydrology 1980. Low Flow Studies report. Wallingford, UK.
Klaassen, B.E. & Pilgrim, D.H. 1975. Hydrograph recession constants for New South Wales streams.
Civ. Engng Trans. Instn Engrs, Australia, 1975, 43-49.
Meigh, J.R. 1987. Low flow analysis of selected catchments in Malawi and Zimbabwe. Preliminary
report on the Basement Aquifer Project, Institute of Hydrology, Wallingford, UK.
Nathan, R.J. & McMahon, T.A. 1990(a). Evaluation of automated techniques for base flow and
recession analyses. Wat. Resour. Res. 26, 7, 1465-1473.
National Water and Soil Conservation Authority 1984. An index for base flows. Streamland 24, Water
and soil directorate, Ministry of Works and Dev., Wellington, N.Z.
Pilon, P.J. & Condie, R. 1986. Median drought flows at ungauged sites in Southern Ontario. Canadian
Hydrology Symposium (CHS86), National Research Council of Canada, Regina.
Pirt, J. & Douglas, R. 1982(b). A study of low flows using data from the Severn and Trent catchments.
J. Instn Wat. Engrs Scient. 36, 4, 299-309.
Tallaksen, L. 1986. An evaluation of the Base Flow Index (BFI). Dept. of Geography, University of
Oslo.
Wright, C.E. 1974. The influence of catchment characteristics upon low flows in South East England.
Water Services, July 1974, 227-230.